A New Weighted Metric: the Relative Metric II

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In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.
23 pages, 2 figures

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Metric Geometry, Classical Analysis and ODEs, Primary 39B62, Secondary 26D07, 30F45

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http://salesiana.dossiersoluciones.com/handle/123456789/61966

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108026
 http://arxiv.org/abs/math/0108026

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arXiv